Find a linear differential operator
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)
For,
1+6x - 2x^3
and,
e^-x + 2xe^x - x^2e^x
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Five years ago a company earned $1.50 for each share (EPS = $1.50). Its earnings this year were $3.20. Determine the growth rate in earnings per share (EPS) over the 5-year period.
The football of the preceeding exercise is released( from rest) at an altitude of 16.3m. Find its final velocity and time of fall.
Make up an example of a problem which features the terms below, and solve them. It can be a extremely simple straightforward problem.
Solve the given differential equation by using the substitution u=y' (Use C1 and C2as arbitrary constants. Use x as the independent variable.)
Suggest: f : R----> R is continuous, a, b are functions from R to R and are differentiable on R. g(x) = integral of f(t)dt with upper limit = b(x) and lower limit = a(x) the problem is to determine a general formula for the derivative of g at x
Prove the validity of the limit lim x->x_0 (ax+b)=ax_0+b by converting to a statement about sequences.
Use the method of variation of parameters to determine a general solution to differential equation: ty''+(1-2t)y'+(t-1)y=te^t given that y1=e^t and y2=e^t (ln t) are two linearly independent solutions to the corresponding homogenous equation.
How can you find the number of possible outcomes of a playoff between two teams where the first team to win four games wins the playoff?
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